You are confusing two things: the distribution of items in a shuffle vs. the distribution of the shuffles themselves.

To shuffle n items, you need n pseudo-random integers; this amounts to n distinct states per shuffle, which is less than the 2n available states to a PRNG.

However, to generate the ensemble of permutations of n elements via random shuffles, as you correctly point out, you'd need n! states, which is greater than 2n for all n > 3.

Edit: However, note that common PRNGs have 231 states or more. 11! < 231 < 12!, so the distribution of events taken from the ensemble of shuffles of 11 elements or less should be normal if the underlying PRNG is normally-distributed.

Footnote: For the record, the main rationale for adding "random.shuffle()" to the standard library was that it's so darn easy to get this wrong, even if you're well aware of the general "let's swap them all" approach.